Global oscillations in low-density round jets with parabolic velocity profiles

Abstract

Experiments and spatiotemporal stability analysis are carried out to study the global oscillations in laminar low-density round jets with parabolic velocity profiles. The experimental results of laminar low-density jets with parabolic velocity profiles exhibit global axisymmetric oscillations. The spatiotemporal stability results based on base profiles from numerical simulations are consistent with the present experimental results. These results differ from the prediction of stability study by Coenen et al. (Phys. Fluids, vol. 20, 2008, p. 074104). They reported that the low-density jets with near parabolic velocity profiles show global helical oscillations. It is observed that the method used by Coenen et al. is not able to predict the nature of global oscillations observed in experiments for low-density jets with near parabolic profiles. The present spatiotemporal stability results demonstrate that the base flows from Navier–Stokes equations are required to predict the critical conditions observed in experiments for low-density jets with near parabolic velocity profiles. The breakdown distance of globally unstable low-density jets scales with $(Re-Re_c)^{-1/2}$ ( $Re_c$ is the critical Reynolds number), consistent with the scaling law obtained from the nonlinear global mode of the Ginzburg–Landau equation.

Chaos via type-II intermittency in a forced globally unstable jet

“…Shown in figure 1(a), the facility consists of a nozzle assembly, a helium supply system, and electronics for data acquisition and external forcing. The nozzle assembly contains a convergent section (area ratio of 100:1) with a round outlet of diameter D = 6 mm and extension length L = D. For an axisymmetric jet in the incompressible inertial regime, the onset of global instability is known to be determined by three primary parameters (Hallberg & Strykowski 2006;Coenen et al 2017;Chakravarthy et al 2018;Nair et al 2022): (i) the jet Reynolds number, Re ≡ ρ j U j D/μ j , where ρ j and μ j are the density and dynamic viscosity of the jet fluid, while U j is the jet centreline velocity; (ii) the jet-to-ambient density ratio, S ≡ ρ j /ρ ∞ , where ρ ∞ is the density of the ambient fluid; and (iii) the transverse curvature, D/θ 0 , where θ 0 is the initial momentum thickness. In this study, we focus on a parameter combination (Re = 648, S = 0.14, D/θ 0 = 31.1) just beyond the Hopf point, where an axisymmetric global mode exists at a natural frequency of f n = 497 ± 5 Hz.…”

“…2018; Nair et al. 2022): (i) the jet Reynolds number, , where and are the density and dynamic viscosity of the jet fluid, while is the jet centreline velocity; (ii) the jet-to-ambient density ratio, , where is the density of the ambient fluid; and (iii) the transverse curvature, , where is the initial momentum thickness. In this study, we focus on a parameter combination (, , ) just beyond the Hopf point, where an axisymmetric global mode exists at a natural frequency of Hz.…”

“…In the absence of counterflow, a jet whose density is similar to that of its surroundings is dominated by local convective instability, behaving as a spatial amplifier of extrinsic disturbances (Huerre & Monkewitz 1990). By contrast, a jet whose density is below a critical value can develop a large enough region of local absolute instability to become globally unstable, behaving as a self-excited oscillator with an intrinsic hydrodynamic mode (Chomaz, Huerre & Redekopp 1988;Monkewitz et al 1990;Hallberg & Strykowski 2006;Lesshafft & Marquet 2010;Coenen et al 2017;Chakravarthy, Lesshafft & Huerre 2018;Nair, Deohans & Vinoth 2022). In nonlinear dynamics, this can be viewed as a transition from a fixed point to a limit cycle, which can occur via a supercritical or subcritical Hopf bifurcation (Zhu, Gupta & Li 2017;Lee et al 2019;.…”

“…1990; Hallberg & Strykowski 2006; Lesshafft & Marquet 2010; Coenen et al. 2017; Chakravarthy, Lesshafft & Huerre 2018; Nair, Deohans & Vinoth 2022). In nonlinear dynamics, this can be viewed as a transition from a fixed point to a limit cycle, which can occur via a supercritical or subcritical Hopf bifurcation (Zhu, Gupta & Li 2017; Lee et al.…”

Local linear stability of plumes generated along vertical heated cylinders in stratified environments

“…While non-Boussinesq free plumes, e.g. a fire plume or a helium plume in air, have been found both theoretically and experimentally to exhibit axisymmetric ‘puffing’ modes (Bharadwaj & Das 2017; Chakravarthy, Lesshafft & Huerre 2018; Nair, Deohans & Vinoth 2022), Boussinesq free plumes are characterised by the dominance of swirling helical modes (Marques & Lopez 2014; Chakravarthy et al. 2015).…”